Its also worth pointing out that all large American cities aren't equal in terms of crime stats - NYC is (surprisingly, to many people) among the safest. I can remember reading headlines within the last decade about London notably reaching a higher murder rate, despite London presumably having something closer to total prohibition of firearms.
TV shows here love to portray NYC as a Gotham-esque hellscape because that makes for good police procedurals, but in reality I'd bet if you invented some kind of metric comparing TV portrayals of violent crimes against actual violent crime stats NYC would have the largest gap between fiction and reality.
Don't get me wrong, horrific stuff happens here. There are millions upon millions of people, some of them awful to others. But by the numbers its safer than almost every other major metro in the country, and solidly middle of the pack among comparable global mega-cities.